Transcript American Intercontinental University

QMB-350
Leah Murray
 Independent

The variable we are basing a prediction on
 Dependent

Response variable
Name the independent and dependent variables
-Hours of studying and grade
-temperature and heating bill
- Age of computer and value
- Size of home and property tax bill
 Positive

Both variables either increase or decrease



Size of house and property tax bill
Temp and air conditioning use
Years of experience and salary
 Negatives

One increases and the other decreases



Age of car and value
Temperature and heating bill
Age and strength
 Strength
of relationship between two
variables
 Correlation coefficient- measures strength of
relationship



Strong: time spent on assignment and grade
Weak: number of sit ups performed and weight
None: Hair color and stats grade
A
graph with the independent variable on the
x axis and the dependent variable on the y
variable
 Visual way to describe the relationship
between two variables
 Measures
both the strength and direction of
the correlation



Close to +1=strong positive relationship
Close to -1=strong negative relationship
Close to 0: No relationship
**This is calculated in excel***
 WARNING:
Just because something has a
strong correlation does NOT mean that there
is causation
 Example:
Shoe size and spelling ability
 Line
placed on a scatter plot to minimize the
distance between the lines and the data
points
 The
line of best fit has an equation with two
components

Slope- how steep the line is and direction of
correlation


Number with the x
Y intercept-where the graph crosses the Y axis

Number all alone
 This
is calculated in excel
Minutes
Grade
20
Time v grade
120
68
30
75
35
72
40
85
60
88
73
90
80
100
Grade
100
80
60
Grade
40
20
0
0
20
40
60
80
Minutes spent on Assignment
100
SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.94343
R Square
0.89006
Adjusted R Square 0.868072
Standard Error
4.129936
Observations
7
ANOVA
df
SS
Regression
1
690.4324
Residual
Total
5
6
85.28185
775.7143
Coefficie
nts
Standard
Error
Intercept
59.90572
3.889456
X Variable 1
0.469408
0.073779
MS
690.432
4
17.0563
7
F
40.4794
5
t Stat
15.4020
8
6.36234
6
P-value
2.09E05
0.00141
8
Significanc
eF
0.001418
Lower 95%
49.90755
0.279753
Upper
95%
69.9038
8
0.65906
3
Lower
95.0%
Upper
95.0%
49.90755
69.90388
0.279753
0.659063
 You
can find the coefficients in the output
 Y=b+ax

B-intercept
A=x variable
Y=59.906+0.469x
**If the x variable is negative we use a – not a + -***
Y

intercept
If the X variable was 0, this would be the value
of the y variable
 Slope

If x increased by 1 unit y would increase (or
decrease) by this many units
 Fill
in a value and solve for the other
variable
 What would you expect your grade to be if
you spent 65 minutes on the assignment
I
received an 90 on the assignment, how
long did I spend working on the assignment
**No predictions are absolute***
 Making
predictions outside of the bounds of
the data


Example if you have a bunch of data about
heights and weights of children 2-4 years old you
cannot use the equation to predict the weight of
a 30 year old based on height
If we have data that predicts heating bills based
on temperature for temperatures in the 0-30
range we cannot expect the equation to give us a
good prediction for a 70 degree day
 How
much of the dependent variable is
explained by the independent variable and
the regression line
 Symbol:
 Found in excel output
 R Square
 0.89
 What does it mean? 89% of your grade is
explained by the time you spent on it
 **We want values close to 1 or 100%**
 Standard
deviation of the actual y values
around the predicted y values
 Want this number to be small
Standard Error 4.129936
Smaller numbers mean more consistent
predictions